Basic properties
Modulus: | \(8034\) | |
Conductor: | \(1339\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(68\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1339}(811,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8034.cx
\(\chi_{8034}(31,\cdot)\) \(\chi_{8034}(73,\cdot)\) \(\chi_{8034}(655,\cdot)\) \(\chi_{8034}(811,\cdot)\) \(\chi_{8034}(1555,\cdot)\) \(\chi_{8034}(1981,\cdot)\) \(\chi_{8034}(2257,\cdot)\) \(\chi_{8034}(2293,\cdot)\) \(\chi_{8034}(2335,\cdot)\) \(\chi_{8034}(2449,\cdot)\) \(\chi_{8034}(2803,\cdot)\) \(\chi_{8034}(3385,\cdot)\) \(\chi_{8034}(3505,\cdot)\) \(\chi_{8034}(3541,\cdot)\) \(\chi_{8034}(3739,\cdot)\) \(\chi_{8034}(3853,\cdot)\) \(\chi_{8034}(4009,\cdot)\) \(\chi_{8034}(4363,\cdot)\) \(\chi_{8034}(4399,\cdot)\) \(\chi_{8034}(4519,\cdot)\) \(\chi_{8034}(5689,\cdot)\) \(\chi_{8034}(5881,\cdot)\) \(\chi_{8034}(6001,\cdot)\) \(\chi_{8034}(6157,\cdot)\) \(\chi_{8034}(6583,\cdot)\) \(\chi_{8034}(6661,\cdot)\) \(\chi_{8034}(7093,\cdot)\) \(\chi_{8034}(7129,\cdot)\) \(\chi_{8034}(7249,\cdot)\) \(\chi_{8034}(7561,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{68})$ |
Fixed field: | Number field defined by a degree 68 polynomial |
Values on generators
\((5357,1237,5773)\) → \((1,-i,e\left(\frac{7}{34}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 8034 }(811, a) \) | \(1\) | \(1\) | \(e\left(\frac{65}{68}\right)\) | \(e\left(\frac{5}{68}\right)\) | \(e\left(\frac{55}{68}\right)\) | \(e\left(\frac{31}{34}\right)\) | \(e\left(\frac{15}{68}\right)\) | \(e\left(\frac{15}{34}\right)\) | \(e\left(\frac{31}{34}\right)\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{33}{68}\right)\) | \(e\left(\frac{1}{34}\right)\) |